Chemical Engineering September 2020 - 35

Table 1. MeasureMenT and Model adapTaTion resulTs for saMple puMp
Variable
Q1
P1
I2
N3
P4
Δ Efficiency1
Δ Head1
unit
m3/s
kPa
A
rpm
kPa
-
-
raw
0.120
100
117.0
3,580
2,600
1.0
1.0
fied to describe the nominal performance
of the specific equipment.
All required topology and model
parameters are stored in a central
cloud database to be accessible by
the analytics algorithms.
Both process data and equipment
modeling suffer from some degree
of error, either random or systematic.
A data-reconciliation method
is applied, inspired by applications
in chemical and power plants [1].
Such methods are able to evaluate
non-linear models of equipment.
They rely on data redundancies (that
is, sensor values, equipment topology
and physical equations), to optimally
adjust measured quantities
and model parameters by respecting
problem constraints and conservation
equations. This method
derives the most probable operating
conditions of both the complete system
and of individual components
(pumps, motors, pipes, valves and
so on). This global approach reduces
the level of uncertainty for
every evaluated timestamp
and derives customized
component characteristics
according to the latest status
of the equipment. Any
general data reconciliation
procedure must solve
the following constrained
least-squares problem;
that is, to minimize Equation
(1) subject to the constraint
of Equation (2):
Minimize:
J ( ŷ , ẑ ) = ( y - ŷ )T V-1 ( y - ŷ )
(1)
Subject to:
Ay ŷ + Az ẑ = 0
(2)
450
425
400
375
350
325
300
275
250
0.00
0.02
0.04
0.06
Flow, m3/s
Figure 5. This graph shows the comparison between
sensor data and the nominal curve and recommended
operating regions
ChemiCal engineering www.Chemengonline.Com September 2020
0.08
0.10
Adapted
0.121
100
116.1
3,580
2,626
0.824
0.945
Δ
0.83%
-0.04%
-0.77%
0.00%
1.00%
-17.60%
-5.50%
Confidence
95%
95%
95%
95%
95%
80%
80%
www.ekato.com
1 (superscript) model parameters correcting the nominal pump performance (efficiency and head coefficient)
Where, y and z are the raw measured
and non-measured parameters,
ŷ and ẑ are the adapted
parameters respectively, A is the incident
and V the variance matrices.
A simplified example is shown
in Figure 4, where a number of
measurements are available for
a pump/electrical driver system.
One can also take into account the
physical modeling equations that
describe the expected behavior
of the system. In such a case, an
overdetermined system is derived,
where measurements will not fit
the nominal expected behavior of
the components. A data-reconciliation
method is applied and Table
1 illustrates the corresponding results.
It is noted that depending on
the amount of confidence given to
measurements and model parameters,
the adaptation results can
vary. In this example, higher confidence
is given to measured values
and lower to model parameters,
VERTICAL DRYERS
FOR SOLIDS
FROM PASTY TO FREE FLOWING
n MINIMUM POWER INPUT
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DISTRIBUTION
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DISCHARGE DURING EMPTYING
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Chemical Engineering September 2020

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